В этой категории варианты Задачи 10, раздела "Пределы" в задачнике Кузнецова Л.А.
Вычислить предел функции:
Показана 31 страница из 31, находящейся в данной категории.
![{\displaystyle \lim _{x\to -8}{\frac {{\sqrt {1-x}}-3}{2+{\sqrt[{3}]{x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3590189ffcda962ec34f3530b434fc5b8c4085a9)
![{\displaystyle \lim _{x\to 1}{\frac {\sqrt {x-1}}{\sqrt[{3}]{x^{2}-1}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/54509eef30aa870dbcdf0ad1f897b110993c1956)
![{\displaystyle \lim _{x\to -2}{\frac {{\sqrt[{3}]{x-6}}+2}{x^{3}+8}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cafc384bd7f0e02c7f54c44d9b0256d7b7aa6460)
![{\displaystyle \lim _{x\to 16}{\frac {{\sqrt[{4}]{x}}-2}{{\sqrt {x}}-4}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7507b6662312d60f13d12b528693cfb3b16b126f)
![{\displaystyle \lim _{x\to 8}{\frac {{\sqrt {9+2x}}-5}{{\sqrt[{3}]{x}}-2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a2e670aea96d958359bde73facd487d811fa6b6f)
![{\displaystyle \lim _{x\to 0}{\frac {{\sqrt[{3}]{8+3x+x^{2}}}-2}{x+x^{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5b371ed72d393165e1954075829fd191cb2d6db8)
![{\displaystyle \lim _{x\to 0}{\frac {{\sqrt[{3}]{27+x}}-{\sqrt[{3}]{27-x}}}{x+2{\sqrt[{3}]{x^{4}}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a38db93a04a47b36b5c3d7d1e1cfc99757d6c801)
![{\displaystyle \lim _{x\to 1}{\frac {{\sqrt[{3}]{x}}-1}{{\sqrt {1+x}}-{\sqrt {2x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1b93a5b315600fd49bf584bb6c89c2c2a978a5a)
![{\displaystyle \lim _{x\to 0}{\frac {{\sqrt {1+x}}-{\sqrt {1-x}}}{{\sqrt[{3}]{1+x}}-{\sqrt[{3}]{1-x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e75ebed62da01a62182de1cc823cb71711edca05)
![{\displaystyle \lim _{x\to 2}{\frac {{\sqrt[{3}]{4x}}-2}{{\sqrt {2+x}}-{\sqrt {2x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8c324db89bf427c14adb7d3799916752be2e0195)
![{\displaystyle \lim _{x\to 3}{\frac {{\sqrt[{3}]{9x}}-3}{{\sqrt {3+x}}-{\sqrt {2x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/76b0f68ba1626b0359aa63b0f4f97035943cb9b6)
![{\displaystyle \lim _{x\to -2}{\frac {{\sqrt[{3}]{x-6}}+2}{x+2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b7a81c42d3c9785c87845d769bc0a77fa6dda108)
![{\displaystyle \lim _{x\to 4}{\frac {{\sqrt[{3}]{16x}}-4}{{\sqrt {4+x}}-{\sqrt {2x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fcf996f1c85d321e414f76bdc61dc42f16437e87)
![{\displaystyle \lim _{x\to 8}{\frac {{\sqrt {9+2x}}-5}{{\sqrt[{3}]{x^{2}}}-4}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c7d91803e14a3991d2b10c56527e20d1a0ac1a3b)
![{\displaystyle \lim _{x\to {\frac {1}{2}}}{\frac {{\sqrt[{3}]{\frac {x}{4}}}-{\frac {1}{2}}}{{\sqrt {{\frac {1}{2}}+x}}-{\sqrt {2x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6447d328fad78bc93968dd4b9392227903f35c69)
![{\displaystyle \lim _{x\to {\frac {1}{3}}}{\frac {{\sqrt[{3}]{\frac {x}{9}}}-{\frac {1}{3}}}{{\sqrt {{\frac {1}{3}}+x}}-{\sqrt {2x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7fb103a74334e2a9d24c55046de49c5cb6d05ace)
![{\displaystyle \lim _{x\to {\frac {1}{4}}}{\frac {{\sqrt[{3}]{\frac {x}{16}}}-{\frac {1}{4}}}{{\sqrt {{\frac {1}{4}}+x}}-{\sqrt {2x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/93ca65f85fd36b0f60316b30af57a8dad7cf817b)
![{\displaystyle \lim _{x\to 0}{\frac {{\sqrt {1+x}}-{\sqrt {1-x}}}{\sqrt[{7}]{x}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8107a56584e13a5ce61c0b1088caf5d8e50b1f88)
![{\displaystyle \lim _{x\to 0}{\frac {{\sqrt[{3}]{27+x}}-{\sqrt[{3}]{27-x}}}{{\sqrt[{3}]{x^{2}}}+{\sqrt[{5}]{x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d3b6134694ad4622e1eae8a472000a72d873dee4)
![{\displaystyle \lim _{x\to 0}{\frac {{\sqrt[{3}]{8+3x-x^{2}}}-2}{\sqrt[{3}]{x^{2}+x^{3}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff873a1fc5ce8735703f8bd2438a5eaab5ac4c13)
![{\displaystyle \lim _{x\to 0}{\frac {{\sqrt {1-2x+3x^{2}}}-(1+x)}{\sqrt[{3}]{x}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/315605d4637d9fec7465b9b7e0a73a06eee9c752)
![{\displaystyle \lim _{x\to 16}{\frac {{\sqrt[{4}]{x}}-2}{\sqrt[{3}]{({\sqrt {x}}-4)^{2}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e5a9891e03f6b8b401b953603708510142ad0892)
![{\displaystyle \lim _{x\to -2}{\frac {{\sqrt[{3}]{x-6}}+2}{\sqrt[{3}]{x^{3}+8}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0c824e3bb436c4a989c0a66111ff4538bc64fab9)
![{\displaystyle \lim _{x\to 4}{\frac {{\sqrt {x}}-2}{\sqrt[{3}]{x^{2}-16}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b34fd0115484e285ac4b46a0a9fac91f2ba759cb)
![{\displaystyle \lim _{x\to -8}{\frac {10-x-6{\sqrt {1-x}}}{2+{\sqrt[{3}]{x}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4a2dda9a2fb07c17d049e3af3d3f8a1678362c79)
![{\displaystyle \lim _{x\to 3}{\frac {{\sqrt {x+13}}-2{\sqrt {x+1}}}{\sqrt[{3}]{x^{2}-9}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5239d2041faa8e2029c2e6b8a855add7aa7ada22)